Question

Water falls from a height $500 \,m .$ The rise in temperature of water at bottom if whole of the energy remains in water, will be : (specific heat of water is $c=4.2\, kJ / kg$ )

• A. $0.23^{\circ} C$
• B. $1.16^{\circ} C$
• C. $0.96^{\circ} C$
• D. $1.02^{\circ} C$

Answer 1

Answer: (B)

Potential energy $=$ increase in heat of water.
From law of conservation of energy, we know that energy can neither be created nor destroyed, it remains conserved. When water falls from a height, it has potential energy $(m g h)$, this is used in heating up the water $(m c \Delta \theta)$.
Hence, we have
$m g h=m c \Delta \theta$
$\Rightarrow \Delta \theta=\frac{g h}{c}$
$=\frac{9.8 \times 500}{4.2 \times 10^{3}}=1.16^{\circ} C$